Bài 3: 

\(a,x-\dfrac{2}{5}=0,24\\ =>x-\dfrac{2}{5}=\dfrac{6}{25}\\ =>x=\dfrac{6}{25}+\dfrac{2}{5}\\ =>x=\dfrac{16}{25}\\ b,\left(\dfrac{7}{3}x-0,6\right):3\dfrac{2}{5}=1\\ =>\left(\dfrac{7}{3}x-\dfrac{3}{5}\right):\dfrac{17}{5}=1\\ =>\dfrac{7}{3}x-\dfrac{3}{5}=\dfrac{17}{5}\\ =>\dfrac{7}{3}x=\dfrac{17}{5}+\dfrac{3}{5}=4\\ =>x=4:\dfrac{7}{3}=\dfrac{12}{7}\\ c,\left(2\dfrac{4}{5}x-50\right):\dfrac{2}{3}=51\\ =>\dfrac{14}{5}x-50=\dfrac{2}{3}\cdot51=34\\ =>\dfrac{14}{5}x=34+50=84\\ =>x=84:\dfrac{14}{5}=30\)

Bài 4:

a: \(5\dfrac{4}{7}:x=13\)

=>\(\dfrac{39}{7}:x=13\)

=>\(x=\dfrac{39}{7}:13=\dfrac{3}{7}\)

b: \(6\dfrac{2}{9}x+3\dfrac{10}{27}=22\dfrac{1}{7}\)

=>\(\dfrac{56}{9}x=22+\dfrac{1}{7}-3-\dfrac{10}{27}=19+\dfrac{-43}{189}=\dfrac{3548}{189}\)

=>\(x=\dfrac{3548}{189}:\dfrac{56}{9}=\dfrac{887}{294}\)

c: \(\left(\dfrac{7}{3}x-0,6\right):3\dfrac{2}{5}=1\)

=>\(\left(\dfrac{7}{3}x-0,6\right)=1\cdot3\dfrac{2}{5}=3,4\)

=>\(\dfrac{7}{3}x=3,4+0,6=4\)

=>\(x=4:\dfrac{7}{3}=\dfrac{12}{7}\)

d: \(\left(2\dfrac{4}{5}x-50\right):\dfrac{2}{3}=51\)

=>\(\left(2,8x-50\right)=51\cdot\dfrac{2}{3}=34\)

=>2,8x=34+50=84

=>\(x=\dfrac{84}{2,8}=30\)

e: 

\(\left(4\dfrac{1}{2}-2x\right)\cdot3\dfrac{2}{3}=\dfrac{11}{15}\)

=>\(\left(\dfrac{9}{2}-2x\right)\cdot\dfrac{11}{3}=\dfrac{11}{15}\)

=>\(\dfrac{9}{2}-2x=\dfrac{11}{15}:\dfrac{11}{3}=\dfrac{3}{15}=\dfrac{1}{5}\)

=>\(2x=\dfrac{9}{2}-\dfrac{1}{5}=\dfrac{45}{10}-\dfrac{2}{10}=\dfrac{43}{10}\)

=>\(x=\dfrac{43}{20}\)

a: \(\dfrac{AB'}{AB}=\dfrac{AC'}{AC}\)

=>\(1-\dfrac{AB'}{AB}=1-\dfrac{AC'}{AC}\)

=>\(\dfrac{BB'}{AB}=\dfrac{CC'}{AC}\)

=>\(\dfrac{BB'}{CC'}=\dfrac{AB}{AC}\)

mà \(\dfrac{AB}{AC}=\dfrac{AB'}{AC'}\)

nên \(\dfrac{AB'}{AC'}=\dfrac{BB'}{CC'}\)

=>\(\dfrac{AB'}{BB'}=\dfrac{AC'}{CC'}\)

b: \(\dfrac{AB'}{AB}=\dfrac{AC'}{AC}\)

=>\(1-\dfrac{AB'}{AB}=1-\dfrac{AC'}{AC}\)

=>\(\dfrac{BB'}{AB}=\dfrac{CC'}{AC}\)

a: Xét (O) có

AB,AC là các tiếp tuyến

Do đó: AB=AC

=>A nằm trên đường trung trực của BC(1)

Ta có: OB=OC

=>O nằm trên đường trung trực của BC(2)

Từ (1),(2) suy ra OA là đường trung trực của BC

=>OA\(\perp\)BC

b: Xét (O) có

ΔBCD nội tiếp

CD là đường kính

Do đó: ΔCBD vuông tại B

=>CB\(\perp\)BD

mà OA\(\perp\)BC

nên OA//BD

c: Xét (O) có

OB là bán kính

EB\(\perp\)OB tại B

Do đó: EB là tiếp tuyến của (O)

Ta có: `(a - b)^2 >= 0`

`<=> a^2 - 2ab + b^2 >= 0`

`<=> a^2 + b^2 >= 2ab`

`<=> 2(a^2 + b^2 ) >= a^2 + 2ab + b^2 `

`<=> 2(a^2 + b^2) >= (a+b)^2`

`<=> a^2 + b^2 >= ((a+b)^2)/2`

`<=> a^2 + b^2 >= (4^2)/2`

`<=> a^2 + b^2 >= 16/2`

`<=> a^2 + b^2 >= 8 (đpcm)`

\(a+b\ge4\)

\(\Leftrightarrow\left(a+b\right)^2\ge16\)

\(\Leftrightarrow a^2+b^2+2ab\ge16\left(1\right)\)

\(\left(a-b\right)^2\ge0\)

\(\Leftrightarrow a^2+b^2-2ab\ge0\left(2\right)\)

\(\left(1\right)+\left(2\right)\Rightarrow2\left(a^2+b^2\right)\ge16\)

\(\Rightarrow a^2+b^2\ge8\left(dpcm\right)\)

Mn ơi giải giúp em với 

`527 + {[2 . (2 . 2^3 + 3^2 + 4^2 - 5^2) + 678^0]^3 : 33^2}`

`= 527 + {[2 . (16 + 9 + 16 - 25) + 1]^3 : 33^2}`

`= 527 + {[2 . (25 + 16 - 25) + 1]^3 : 33^2}`

`= 527 + {[2 . 16  + 1]^3 : 33^2}`

`= 527 + {[32  + 1]^3 : 33^2}`

`= 527 + {33^3 :33^2}`

`= 527 + 33^(3-2)`

`= 527 + 33`

`= 560`

\(\dfrac{4}{9\cdot11}+\dfrac{4}{13\cdot15}+...+\dfrac{4}{95\cdot97}+\dfrac{4}{97\cdot99}\\ =2\cdot\left(\dfrac{2}{9\cdot11}+\dfrac{2}{13\cdot15}+...+\dfrac{2}{95\cdot97}+\dfrac{2}{97\cdot99}\right)\\ =2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{95}-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{99}\right)\\ =2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\\ =2\cdot\dfrac{11-1}{99}\\ =2\cdot\dfrac{10}{99}\\ =\dfrac{20}{99}\)

Sửa đề: `S = 4/(9.11) + 4/(11.13) + ... + 4/(97.99)`

`S = 2 . (2/(9.11) + 2/(11.13) + ... +2/(97.99))`

`S = 2 . (1/9 - 1/11 + 1/11 - 1/13 + ... + 1/97 - 1/99)`

`S = 2 . (1/9 - 1/99)`

`S = 2 . (11/99 - 1/99)`

`S = 2 . 10/99 `

`S = 20/99`

\(\left(\dfrac{3}{2}\right)^5\cdot x=\left(\dfrac{3}{2}\right)^7\)

=>\(x=\left(\dfrac{3}{2}\right)^7:\left(\dfrac{3}{2}\right)^5=\left(\dfrac{3}{2}\right)^2=\dfrac{9}{4}\)

a: M là trung điểm của AB

=>\(MA=MB=\dfrac{AB}{2}=6\left(cm\right)\)

N là trung điểm của MA

=>\(AN=NM=\dfrac{AM}{2}=1,5\left(cm\right)\)

P là trung điểm của MB

=>\(MP=PB=\dfrac{MB}{2}=\dfrac{3}{2}=1,5\left(cm\right)\)

NP=MN+MP

=1,5+1,5=3(cm)

b: \(NP=NM+MP\)

\(=\dfrac{1}{2}\left(MA+MB\right)\)

\(=\dfrac{1}{2}\cdot AB=3\left(cm\right)\)

\(\left(\dfrac{2}{3}\right)^8:x=\left(\dfrac{2}{3}\right)^2\)

=>\(x=\left(\dfrac{2}{3}\right)^8:\left(\dfrac{2}{3}\right)^2=\left(\dfrac{2}{3}\right)^6=\dfrac{64}{729}\)